Cross-Asset Pair Signals for Adversarial Markets
Statistical arbitrage from supply-chain position, the cointegration test discipline, and the input/output long-short structure.
When two assets move together, what are they both standing on?
They are standing on the same cost. An upstream manufacturer and its downstream consumer share a single variable — the price of the input one makes and the other buys. When that variable moves, both equity prices respond: one margin expands, the other compresses. The spread between the two prices is not a statistical coincidence. It is the structural signal the market has not yet closed.
The 06-19 lesson named the regime and built the detector. This lesson names what to trade when the regime fires. The pair signal is the instrument. The supply-chain position is the prior that separates valid pairs from spurious ones. The cointegration test is the gate that validates the statistical relationship. The z-score is the trigger.
§ IFrame
The 06-19 regime-detector produces a state label — trending, mean-reverting, or transitional — and a persistence estimate. What the lesson left open: which position to take when the regime fires. The pair signal fills that gap. Two equities structurally linked by a supply-chain cost relationship share a common stochastic driver. The spread between them is the tradeable entity.
The three-step protocol is the architecture. First: screen pairs by supply-chain structure. The structural screen reduces the N(N-1)/2 candidate pair space to a set grounded in fundamental logic. Second: validate cointegration statistically. The Engle-Granger two-step tests whether the spread is stationary. Third: trade the spread z-score. The z-score normalizes the current spread against its historical distribution and produces the entry trigger.
§ IIFoundations
What cointegration means in operational terms
Two price series X and Y are cointegrated when the linear combination Y − β·X produces a residual series ε whose mean and variance do not drift over time. A stationary ε returns to its mean after each deviation. Trading the stationary spread is the market-neutral position: long the underperforming leg, short the outperforming leg, close when the spread reverts. Aldridge's treatment of statistical arbitrage strategies (Ch 8, pp. 211–213) frames this directly — the pair trade bets on the relationship, not the direction of either individual asset.
Why supply-chain position creates structurally valid pairs
Two assets that test as cointegrated in a mining exercise may be spuriously linked. Supply-chain position provides the fundamental prior: when one entity's output is another entity's material input, both share the same cost driver. A shock to that driver changes both margins simultaneously — expanding one and compressing the other. The spread widens. The reversion is mechanical, not statistical.
The input/output long-short structure
The trade direction follows from chain position. The upstream entity — the one that makes the scarce input — captures margin when input prices rise. The downstream entity absorbs the cost and loses margin. The long leg is always the upstream entity; the short leg is always the downstream entity. This is the input/output long-short structure. It is a spread trade: long the winning margin, short the losing margin, hold until the gap closes.
§ IIIMechanism
Step 1 — Screen by supply-chain structure
Build the candidate pair list from fundamental analysis. The list is not generated algorithmically — it is authored. Each entry carries: long ticker, short ticker, the specific input resource that links them, and a notes field naming the cost mechanism. Typically 15 to 40 pairs for a given investment universe.
Step 2 — Validate cointegration with the Engle-Granger two-step
- Regress the downstream price (Y) on the upstream price (X): Y = β₀ + β₁·X + ε
- Extract the residual series ε
- Run the Augmented Dickey-Fuller test on ε
- Promote to active pair when ADF p-value < 0.05 over the lookback window
Step 3 — Trade the spread z-score
Normalize: z = (ε_current − μ_spread) / σ_spread. Entry: short the spread at z > +2.0; long the spread at z < −2.0. Exit: close when |z| < 0.5. Four calibration parameters per pair: lookback window (60–252 days), entry z-score threshold, exit threshold, and hold-time cap.
§ IVWorked Example
The AI-capex case. Micron Technology (MU) as long leg, Apple Inc. (AAPL) as short leg. Micron manufactures HBM and DRAM. Apple purchases DRAM for device memory. When AI-datacenter demand drives DRAM contract prices up 80–90%, Micron's cost basis is fixed while Apple's materials cost rises. The structural prediction: the spread widens as MU's margin expands and AAPL's compresses.
def test_cointegration(
x_prices: np.ndarray,
y_prices: np.ndarray,
adf_threshold: float = 0.05,
) -> CointegrationResult:
result = OLS(y_prices, add_constant(x_prices)).fit()
spread = result.resid
adf_stat, adf_pvalue, *_ = adfuller(spread, maxlags=1)
return CointegrationResult(
adf_pvalue=adf_pvalue,
beta=result.params[1],
spread_mean=float(spread.mean()),
spread_std=float(spread.std()),
is_valid=adf_pvalue < adf_threshold,
)The beta, spread_mean, and spread_std fields are stored at end of day. The intraday signal reads stored parameters rather than re-running the regression on each tick.
§ VConnection to Prior Lessons
06-19 regime detection. The pair signal operates best in a mean-reverting regime. The hysteresis buffer from that lesson applies here: do not enter a pair trade within the first 3 days of a regime transition. A transition to trending means the spread will widen rather than revert.
06-12 strategy attribution. IR > 1.5 over the validation period is the entry gate for live deployment of a new pair. Below that threshold, the pair is paper-tracked until the IR grows or the fundamental logic weakens.
06-04 pre-trade risk gates. Half-Kelly applies per leg, sized against the full pair as a unit. The hold-time cap is the pair's analog of the pre-trade margin calculus — a maximum-duration exit that fires when the spread has not reverted within the expected window.
06-05 live monitoring and kill switch. The pair kill switch fires on spread divergence exceeding three standard deviations. A spread at z = 3.5 with no sign of reversion is a cointegration-breakdown signal. Close both legs.
§ VIConnection to Today's Dev Lesson
The Rust lesson takes the protocol above and implements it as a lazy pipeline. flat_map generates pairs one at a time without allocating all N(N-1)/2 candidates in memory. filter_map gates on cointegration validity and z-score entry in the same pass. collect() materializes only the signals that clear both gates.
The CointegrationStore in the Rust lesson holds the fields that test_cointegration returns here — beta, spread_mean, spread_std. The two lessons share a data contract: this lesson defines what must be stored; the Rust lesson shows how to retrieve it at scale.
§ VIIClosing
The pair signal is the structural edge that supply-chain intelligence provides. Individual asset direction is noise; spread between structurally linked assets is the signal. The three-step discipline filters at every stage: structural screen before statistical test, statistical test before z-score entry, z-score entry before position fill, position fill under two-leg discipline.
The input/output long-short structure generalizes. Every market sector with identifiable supply chains has pair candidates. The AI-capex case is one instance. The methodology is the pattern.
Examine this. Apply it to the next structural observation that arrives.